In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-
state stability (ISS) for infinite-dimensional systems. This property allows for the estimation of …

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-
dimensional control systems, including some classes of evolution equations over Banach …

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In this work, the relation between input-to-state stability and integral input-to-state stability is
studied for linear infinite-dimensional systems with an unbounded control operator. Although …

This paper is devoted to two issues. The first one is to provide Lyapunov-based tools to
establish integral input-to-state stability (iISS) and input-to-state stability (ISS) for some …

We introduce a new concept of ℓ∞-input-to-state stability for infinite networks composed of a
countable set of interconnected nonlinear subsystems of ordinary differential equations. We …

This paper studies the input-to-state stability (ISS) properties for a class of semi-linear
parabolic partial differential equations (PDEs) with respect to boundary disturbances. In …

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform
global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances …

In this article, we provide several characterizations of integral input-to-state stability (iISS) of
time-delay systems. These characterizations differ in the way the considered Lyapunov …

We study minimal conditions under which mild solutions of linear evolutionary control
systems are continuous for arbitrary bounded input functions. This question naturally …